This is the Knot Tieing Bot. It is as far as I know the first lego robot that can tie a knot. The knot that it ties is known as a Simple Knot, Overhand Knot, Common Knot, or Thumb Knot. How it works is it first crosses over the two ends then picks up the end it moved first and place it in the circle made by crossing the two ends. Then it picks up the very top of the circle and pulls it back and over the end in the middle, doing this makes the knot. The movies show the same thing but from two differen't angles.
There was a challenge posted on the offical Lego Mindstorm website for some one to build a Knot Tying robot. This challenge was up for over a year before I saw it. At the time no one had completed it, so I decided to try it. And after a few failed designs I built KT. If you go here: KT you can view larger pictures of this invention, just click on the sliding pictures on the page.